Identify the range of the function y=-3x+6 when the domain is {-1,2,4}
A. {-6,0,9}
B. {-9}
C. {3,-12,-18}
D. {-3,12}
E. {-6,9}

Distance between Jamal's house and the park = 12 miles

Given distance from Loretta's house to the park = 43 miles

Distance from Loretta's house to Jamal's house = 31 miles.

Jamal's house is in between Loretta's house and the park.

Let 'x' be the distance from Jamal's house to the park.

So the distance between Loretta's house and the park is more than the distance from Jamal's house and the park.

Also the distance from Loretta's house to the park is the sum of the distance from Loretta's house to Jamal's house and the distance from Jamal's house to the park.

i.e., 43 = x + 31

Therefore, x = 43 - 31

                     = 12 miles

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The right angle is called the hypotenuse and the other two sides are called adjacent and opposite.

A right angled triangle is a triangle that has 3 sides and angles. For a right angled triangle, one of the angles is 90 degrees.

The longest side of the triangle is hypotenuse and the other two sides are known as the adjacent and opposite.

Hence in a right triangle, the longest side opposite the right angle is called the hypotenuse and the other two sides are called adjacent and opposite.

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Answer:

7

Step-by-step explanation:

f(x)=4x-5

f(3)=4(3)-5

f(3)=12-5=7

Answer:

a. 105 and 115 employees

b. 185 employees

c. 20 years

Step-by-step explanation:

The total of employees at any given year is y

x is the number of year

then y = 85 + 10x

a. 2nd year: y = 85 + 10(2) = 85 + 20 = 105

  3rd year: y = 85 + 10(3) = 85 + 30 = 115

b. 10th year: y = 85 + 10(10) = 85 + 100 = 185

c: if y = 285

285 = 85 + 10x

10x = 285 - 85

10x = 200

x = 20

Answer:

t=12.5

Step-by-step explanation:

First of you're going to combine liked terms, (5t+3t) to get 8t. You want to get t isolated so you're going to divide it by 8 to get t by itself, you are also going to do 100 divided by 8 because to remain equal you have to do the math on both sides.

Using the average rate of change, it is found that snow was falling at a rate of 0.1 inch an hour during the first period.

This problem is incomplete, but researching it on a search engine, it asks the rate at which snow was falling during the first period.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

From the graph, the first period is until the 10th hour, hence:

The rate is:

r = (2 - 1)/(10 - 0) = 0.1.

Hence snow was falling at a rate of 0.1 inch an hour during the first period.

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The function of g whose graph represents the indicated transformation is g(x) = -|2x| - 1

The function is given as

f(x) = -|8x| - 4

The transformation is given as

A vertical shrink by 1/4

This is represented as

g(x) = 1/4f(x)

So, we have

g(x) = 1/4 * (-|8x| - 4)

Evaluate

g(x) = -|2x| - 1

Hence, the function of g whose graph represents the indicated transformation is g(x) = -|2x| - 1

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According to the given statement the a wire rope sling with a strength of 10,000 pounds and a total working load of 2,000 pounds has a design factor of 5.

Dividing the ultimate (or maximum) stress by both the normal (or working) stress yields a relatively simple equation to determine FoS. A structure but rather component with an FoS of 1 will fail precisely when it meets the design load and is unable to support any extra load.

A wire rope sling, for example, with such a strength exceeding 10,000 pounds (4,545 kilograms) and a total process load of 2,000 pounds (909 kilograms), has a design factor (multiplier) of 5. Currently available wire rope slings have a design factor of 5.

In order to take into account uncertainty regarding the load, the structural qualities, or both, a design factor1 is a tolerance added to a load and structural strength. Design considerations have typically been applied to the size of the load while designing oilfield casing.

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Answer:

The watermelon's price was $7.02

Step-by-step explanation:

83.2 ounces= 5.2 pound

The watermelon that Jose bought weights 5.2 pounds

If 1 pound= $1.35

5.2= $7.02

The commutative property apply to compositions of f(x) and g(x) when f(g(x)) and g(f(x)) are equal for all values of x.

The commutative property says that  [tex]a*b=b*a[/tex] , for any binary operation [tex]'*'[/tex]. These binary operations can be addition, multiplication, function composition, etc. But subtraction and division does not follow commutative property.

Here the operation is composition of two functions defined as,

               [tex](fog) (x)= f(g(x))[/tex]  ,where f and g are two functions.

Then the function composition has commutative property when

                      [tex]fog = gof[/tex].

That is, when f(g(x)) = g(f(x))

This means that the commutative property apply to the composition of functions, f(x) and g(x) when f(g(x)) and g(f(x) are equal for all values of x.

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When 5 is divided by 1/3, we get 15.

Multiplication is an operation that represents the basic idea of repeated addition of the same number.

Given is 5 divided by 1/3.

Assume the result after 5 is divided by 1/3 is equal to [x]. Then, we can write -

x = 5/(1/3) = 15

Therefore, when 5 is divided by 1/3, we get 15.

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Answer:

-21x-13

Step-by-step explanation:

That is all you need

Based on the solution below, we have:

A. a + 2b =5 corresponds to 5. a = 5 - 2b;

B. 5a = 2b  corresponds to 1. a = 2b/5;

C. a + 5 = 2b corresponds to 4. a = 2b - 5;

D. 5(a + 2b) = 0 corresponds to 3. a = -2b; and

E. 5a + 2b=0 corresponds to 2. a = -2b/5.

For clarity purposes, the equations in the question are restated as follows:

A. a + 2b = 5                1. a = 2b/5

B. 5a = 2b                   2. a = -2b/5

C. a + 5 = 2b               3. a = -2b

D. 5(a + 2b) = 0          4. a = 2b-5

E. 5a + 2b =0              5. a = 5-2b

A. From the equation a + 2b = 5, a can be solved as follows:

a + 2b = 5

a = 5 - 2b

B. From the equation 5a = 2b, a can be solved as follows:

5a = 2b

a = 2b/5

C. From the equation a + 5 = 2b, a can be solved as follows:

a + 5 = 2b

a = 2b - 5

D. From the equation 5(a + 2b) = 0, a can be solved as follows:

5(a + 2b) = 0

5a + 10b = 0

5a = -10b

a = -10b/5

a = -2b

E. From the equation 5a + 2b =0, a can be solved as follows:

5a + 2b =0

5a = -2b

a = -2b/5

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Answer:

Lydia is preparing financial statements for her company. Who would be interested in the information provided in these financial statements? Financial statements are of prime importance to Investors  who will use the information to buy or sell stocks of the company. These statements are also inspected by an auditor to look into any irregularities or fraud in the book of accounts.

Step-by-step explanation:

Investors

Investors are individuals or firms who offer capital to a business in exchange for a share in ownership and profits. They are external users of financial statements. Investors use financial statements to know what returns to expect from their investments. Existing and potential investors rely on financial reports to decide on whether to buy or sell their shares.

Auditor

An auditor is a skilled individual authorized to assess, evaluate, and validate financial statements' accuracy as prepared by a company.  The auditor reviews and gives a professional and independent opinion on the company's financial affairs.

So Katya needs 21.42 gallons of gas for 600 miles.

A Linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Given we have Katya have to take a trip for 600 miles.

Let x be number of gallons of gas y be number of miles driven by Katya

We have an relation from table that 28X = Y and Y we have from table 600

So 28X = 600 and [tex]X = \frac{600}{28}[/tex]

X= 21.42 gallons .

Therefore Katya needs 21.42 gallons of gas for 600 miles.

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Answer:

Step-by-step explanation:

6x-5y=30. Answer Hope it helps

Supplementary angles are two angles whose measures add up to 180°. If An angle is 134.2 then other angles are 22.9.

Supplementary angles are two angles whose measures add up to 180°

Supplementary angles are those that add up to 180.

supplementary angle: x

an angle: x+134.2

and together they must measure 180:

x+x+134.2 = 180

2x+134.2=180

2x=180-134.2

2x=45.8

x=22.9

This is the supplementary angle the other angle is 22.9+134.2 = 157.1

Thus the the angle of each is 22.9.

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Step-by-step explanation:

A bank offered a money market account with an APY of 3.227%.

A) If interest is compounded monthly, what is the equivalent annual nominal rate?

B) If you wish to have $10,000 in this account after 6 years, what equal deposit should

you make each month?

The closest approximation of (√2 + √5)² is 13.

If you want to round to one or two decimal places, look at the digit immediately after the decimal point. To the right of the necessary place value digit, draw a vertical line. Observe the following digit. Increase the preceding digit by one if the next digit is 5 or higher.

According to the question, we are Given,

(√2 + √5)²

⇒ 2 + 5 + 2(√2)(√5)                                      (using (a+b)² = a² + b² + 2ab)

⇒ 7 + 2√10

⇒ 7 + 2 × 3.16

⇒ 7 + 6.3

⇒13.3

So, our answer is closest to 13.

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Answer: (x–2) and (10x+7)

Step-by-step explanation:

10x^2 – 13x – 14=

10x^2 – 20x + 7x – 14=

10x(x–2) + 7(x–2)=(x–2)(10x+7) ==> 3rd option

The type of correlation not associated with scatterplots is called; an indefinite correlation

Correlation is also called dependence and is defined as any statistical relationship, whether causal or not, between two random variables or bivariate data.

Correlation can only be between -1 and 1 but not outside these values.

The types of correlation that we have to include:

no correlation

positive correlation

negative correlation

Hence the type of correlation not associated with scatterplots is an indefinite correlation

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Complete question is;

Which of the following is not a type of correlation associated with scatterplots?

A. no correlation

B. positive correlation

C. negative correlation

D. indefinite correlation

This density in kilograms per pint is 0.946.

Important conversions:

1 gram = 0.001 kilogram

1 ml = 0.001 litres

1 pint = 0.473 litres

1 litre = 2.113 pints

Step 1 : Convert 2 grams per millilitre of volume (2 g/ml) into kilograms per litre (kg/l)

=> (2  x 1000)/ (0.001) = 2 kg / l

Therefore, we get the density in kilograms per litre (kg/l) as 2 kg/l.

Step 2 : Convert the density in kilogram per litre (kg/l) into kilograms per pint (kg/pint)

=> 2 x 0.473 = 0.946 kg/l

Therefore, by converting 2 grams per millilitre of volume into kilograms per pint, we get the density as 0.946 kg/pint.

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The mid point of equation is [tex]m^{2} - 100 = -99[/tex].

The Midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

We have been given that two numbers are 10 units away in different directions from their midpoint, m, on a number line.

The two numbers that are 10 units away indifferent directions would be (m - 10) and(m+10).

The product of both number would be(m -10)(m + 10) .

Since the product of both numbers is -99, so we can represent this information in an equations (m -10)(m + 10) = -99.

Let us simplify our equation using difference of squares[tex](a + b)(a - b) =a^{2} - b^{2}[/tex]

as: [tex]m^{2} - 10^2= -99[/tex]

[tex]m^{2} - 100 = -99[/tex]

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The diameter is 18 inches.

It should be noted that the area of a circle is represented by πr². This will be:

πr² = 254.34

(3.14 × r²) = 254.34

3.14r² = 254.34

r² = 254.34/3.14

r² = 81

r = ✓81

r = 9

Therefore the diameter will be:

= 2 × radius

= 2 × 9

= 18

The diameter is 18 inches.

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Answer:

The diameter is 18 inches.

Step-by-step explanation:

Area of a circle formula:

A=πr2 (Area equals pi times radius squared)

254.34/3.14  (3.14 substituted for pi)

=81

square root of 81

=9

9x2

=18

Therefore, the diameter is 18 inches.

The measure of the angle x is 22.5 degrees

Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs.

A circle is the locus of all points in a plane which are equidistant from a fixed point

From the given diagram

arc AC = 180 - 135

arcAC = 45 degrees

Since the angle at the vertex is half the intercepted arc, hence;

x = 1/2(arc AC)

x = 1/2(45)

x = 22.5 degrees

Hence the measure of the angle x is 22.5 degrees

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Coordinate plane is the answer of this problem.

A Coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis

We have been given real numbers A number is real that has no imaginary part the set of all real numbers comprises the rational and the irrationals.

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

So therefore an ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the Coordinate plane.

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The exponential functions to the nearest cent :

y = (500)(1.06)^3 is $595.51

y = (20,000)(0.088)^3 is 13,629,44

y = (15,000)(1.05)^5 = 19,144.22

Cent is hundredth value of the dollar. The hundredth term is the second digit to the right of the decimal point. For example, the cent in this amount, $100.11 is 0.01.

In order to round off to the nearest cent, look at the thousandth term, if the number is equal to 5 or greater than 5, add 1 to the hundredth term and the thousandth term becomes 0. For example, $100.527 to the nearest cent is $100.53

In order to round off to the nearest cent, look at the thousandth term, if the number is less than 5, the hundredth term does not change and thousandth term becomes 0. For example, $20. 124 becomes $20.12 to the nearest cent.

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